I don't think the case of Alexander the Great applies to our today's societies.
First of all, science and knowledge in those days were limited to things such as literature, history, logical reasoning and basic arithmetic. Most people couldn't even read and write. So, being literate was enough for someone to become a scholar.
Today, it's way different. Actually, I have been thinking about this for a while. I personally think that we should invent a new system for choosing the head of the state. In fact, I believe the head of the state should not be elected directly by the people.
I believe that every person who holds the nationality of a country should be able to run for becoming the head of the state. However, there should be a series of public exams that filter candidates step by step. Results and scores will be made public. I believe a senior politician needs to know and understand every high school subject in fair depth and knows a bit of some important undergraduate courses. The president should be proficient in mathematics, computer science, physics, chemistry, biology, history, philosophy, logic, literature, psychology, sociology, English (or the lingua franca of the world at the time), business, management, theology and economy.
My idea is that people who think that they can become the head of the state should take part in the national exam that is held in each province/state/federation separately every 5 years. The top 100 people with the highest scores will go to the next level where people can directly cast their votes and select a number of these candidates (depending on the population of the province/state/federation) to represent the interests of their province/state/federation in the parliament. Then the parliament members, who have been through both of these filtering steps and hence are both knowledgeable and popular, will vote to choose someone to run the state for a period of 5 years.
"You can be whatever you want to be. You don't need to be President if you don't want to."
Actually I'm riffing on a song/monologue, "Soliloquy" from the musical Carousel. The antihero has just learned that he is about to become a father and is daydreaming about his future son:
"He might be a champ of the heavyweights,
Or a feller that sells you glue,
--Or President of the United States!
That'd be all right, too.
His mother would like that!
But he wouldn't be President if he didn't wanna be!